geometry

Spirals, fractals, and even bone length proportions whisper of a consistent ratio woven into the universe. Math is hidden in the fabric of things, and when this fact is observed in art, magic happens. Professor, artist, and inventor [John Edmark] draws inspiration from geometric patterns found in nature and builds sculptures using the golden ratio as a standard for design. In this project, he expresses these characteristics through animated biomorphic zoetropes.

[John] modeled several 3D sculptures in Rhino containing similar geometric properties to those found in pinecones and palm tree fronds. As the segments grow from those objects in nature, they do so in approximately 137.5 degree intervals. This spacing produces a particular spiral appearance which [John] was aiming to recreate. To do so, he used a Python script which calculated a web of quads stretched over the surface of a sphere. From each of the divisions, stalk-like protrusions extend from the top center outward. Once these figures were 3D printed, they were mounted one at a time to the center of a spinning base and set to rotate at 550 RPM. A camera then films the shape as it’s in motion at a 1/2000 sec frame rate which captures stills of the object in just the right set of positions to produce the illusion that the tendrils are blooming from the top and pouring down the sides. The same effect could also be achieved with a strobe light instead of a camera.

[John] has more information on his instructables page. He also provides a video of this trick working with an actual artichoke; one of the living examples of the golden ratio which this project was inspired by. Thank you, [Charlie Nordstrom] for helping him document these awesome sculptures and for telling us about them!

Does the image of the clock above make you shutter with fear because of the math you’d need to use to recreate your own version of the project? We certainly understand that High School geometry is becoming a very distant memory, but it’s really not as hard as you think. [Janw] built this analog clock using a graphic LCD and he’s done a great job of explaining the concepts behind it.

The hardware he’s using is pretty standard for an electronic hobby clock; an ATmega16, graphic LCD, DS1307 real-time clock, and supporting hardware like a potentiometer, resistors, and buttons. The code is written in Bascom, but like we said, [Janw] explains the concepts behind drawing the hands on the clock so you can recreate this with any microcontroller or software language you prefer. We recommend grabbing a calculator and some blank paper. It took us a few tries to brush the cobwebs out and really grasp what he’s doing with each equation.

One of the more novel talks we saw at Defcon was [Zac Franken] presenting on access control systems. He covered several different types, but the real fun was his live demo of bypassing a hand geometry scanners like the one pictured above. With the help of two assistants, 4 pounds of chromatic dental alginate, and 5 liters of water, he made a mold of his hand. The box he placed his hand in had markings to show where the pegs on the scanner are located. After 2 minutes he could remove his hand from the cavity. They then filled the mold with vinylpolysiloxane, making sure to remove all bubbles. 20 minutes later the hand was solid and passed the scanner’s test. This may not be a completely practical attack, but it does defeat the overall idea of biometrics; biometrics are built on the assumption that every person is unique and can’t have their features reproduced.

[Zac] also showed an interesting magnetic card spoofer that emulated all three tracks using coils of magnet wire. We hope to see more about that in the future.